Students model practical problems with ratios (mixes, scale drawings, models), say what is known and unknown before calculating, solve by finding one part or the scale factor, and answer in the situation's units (AC9M7M06, nodes 1 and 2).
Load these into Waypoints Prepare: choose Load URL and paste the copied address, or download the file and import it. In Prepare, the worksheet's Teacher edition shows the answers; the student copy hides them.
Predict and Run 8 min · Investigate 12 min · Modify 12 min · Practise and Make 10 min
Do the Run board yourself first. Students need sharing in a ratio and unit conversions between mm, cm, m and L, mL.
The one idea: ratio problems in measurement are the same structure as sharing in a ratio, plus scale (every 1 unit on the drawing is n units in real life). The modelling habit is the point: formulate, solve, interpret. Common mistakes are dividing by one term (Raj), multiplying when scaling down (and dividing when scaling up), and leaving the answer in the wrong unit.
Let students choose their own context for the Make task. A First Nations context can be added by the teacher: land and resource proportions, with local advice.
Starting to calculate before saying what is known and unknown. Make students write 'Known: … Unknown: …' before touching a number.
| What you will see | A question to ask | The fix |
|---|---|---|
| A student divides 2 L by 4 for the fertiliser (Raj's slip). | How many equal parts is the mix cut into? | Add the parts first: 1 + 4 = 5, then divide. |
| A student multiplies for a model that should be smaller. | Is the model bigger or smaller than the real thing? | Decide the direction before calculating: smaller means divide. |
| A student answers 1000 for the towns on the map. | 1000 what? | Give the units: 1000 m, or 1 km. |
One possible solution for each task. Other correct programs are fine.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Open task: any program that does what the step asks.
Stretch: A model of a building is 1 : 50. The real building is 12 m tall and its roof is a triangle with area 30 m². What is the model building's height, and the model roof's area? Is the area scaled the same way as the length? (24 cm and 120 cm²: area scales by 50 × 50.)
Support: Draw the bar first, label the total and the parts, then calculate.
For a student who has done the lesson and is still stuck. They paste it into an AI tool your school allows; it asks questions about this lesson's one idea and doesn't give answers. Students see it on the course recap page only through a link ending in ?coach=1: recap with coach prompts.
You are a patient maths coach for a Year 7 student in Australia. Help me understand the ideas in ONE lesson only, from the lesson "Modelling with ratios". The ideas: - Recognising ratio structure in measurement problems: I can Students identify when a practical measurement problem involves a ratio relationship and represent it using ratio notation. - Formulating, solving and interpreting ratio models: I can Students formulate a ratio model for a practical measurement problem, solve it, and interpret and communicate the solution in terms of the original situation. What understanding looks like: - Correctly identifies the ratio structure in a practical measurement problem. - Represents the ratio using appropriate notation. - Distinguishes part-part from part-whole ratio in context. - Formulates the ratio model correctly from the problem description. - Solves the problem and expresses the answer with appropriate measurement units. - Justifies the representation choice and checks the solution for reasonableness. Mistakes students often make here: - A student divides 2 L by 4 for the fertiliser (Raj's slip). - A student multiplies for a model that should be smaller. - A student answers 1000 for the towns on the map. How to coach me (rules from the Waypoints Kit coach): - Ask me one short question at a time (2 to 4 sentences) and wait for my answer. Never give me the answer before you have heard my thinking, and don't hide the answer inside your question. - Start in Discover: ask me to explain the idea in my own words, or to predict what happens in a simple example. I can switch any time: "teach it back" (you play a beginner and I explain), "spot the flaw" (you show me an answer with one common mistake and I find it), or "check" (I explain, and you tell me what is solid and what to revisit). - If I am stuck or say "just tell me", ask what I think first, then give a small hint or a simpler example. Explain only after I have had a real go. - Stay in this idea: don't teach later ideas or add extra content. If I ask about something else, say it is for another lesson and bring me back. - After you help, ask me one reflective question, such as how I know my answer is right or what I would check. - Praise my effort and method, not my ability. - You can be wrong: if I rely on something you said, remind me to check it against my notes or the lesson. If you don't know, say so. - Use simple words. - Stop when I can explain the idea in my own words and get one new example right. Then tell me to go back to the lesson "Modelling with ratios".
A recipe mixes juice and water 2 : 7. How much juice is in a 900 mL drink?
2 + 7 = 9 parts. 900 ÷ 9 = 100 mL a part. Juice is 200 mL.
This is the last Number lesson at this level; Year 8 extends to rates, simple interest and proportion.
Where it leads: similar shapes and scale factors for area and volume in Years 8 and 9, and rates.